GEOMETRY
What is the perimeter of a square that has an area of 25?
20
If x-2 = 64, what is the value of x1/3 + x0?
3/2
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24.
Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
If (23)2 = 4p, then 3p =
27
In how many different ways can five students be seated in three chairs?
60 ways
5x4x3=60
What is the area of a circle in which a 3 by 4 rectangle is inscribed?
25pi
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x2. If m is a positive number such that f(7) = g(m) + g(2), what is a possible value of m?
4
Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is
x-25
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?
$10.00
Because $5 + 0.5($10) = $10.
At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, how high would a tree have to be in order to cast a 25-food shadow?
62.5 feet.
Proportional reasoning with similar triangles.
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed? (Calculator needed.)
32,805,000
A boat moored in Richardson Bay (Sausalito) has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?
5 rungs. This number of rungs will be exposed. As the tide comes in, the boat will rise up.
Simplify completely (x + 2)2 - x2
4(x+1)
Note: x2 + 4x + 4 - x2
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4.
1/8 (all heads) + 1/8 (all tails) = 1/4.
If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?
19.
4 + x >9, x + 9 >4, 9+ 4 >x
Possible values of x are: 5 < x < 13
Least possible perimeter: 4 + 5 + 9 = 19
What is the equation of the graph obtained by shifting the graph of y=x2 horizontally to the left 4 units and vertically down 3 units?
y = (x+4)2 - 3
For the system of three equations:
x-z=7 x+y=3 z-y=6
what is x?
8
What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?
10.
Sum of the degree measures of exterior angles is 360.
S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
$8.00.
If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
For how many integer values of b is b+3>0 and 1>2b-9?
Seven.
b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32
x=70, y=38. 70-38=32.